Finsler manifolds with general symmetries

TL;DR

This paper investigates generalized symmetric Finsler spaces, demonstrating that their symmetry-preserving diffeomorphisms form a transitive Lie group and providing existence theorems for such structures.

Contribution

It characterizes the symmetry-preserving diffeomorphisms of generalized symmetric Finsler spaces as a transitive Lie group and establishes foundational existence results.

Findings

Symmetry-preserving diffeomorphisms form a transitive Lie group.

Existence theorems for generalized symmetric Finsler spaces.

Analysis of symmetry properties in Finsler geometry.

Abstract

In this paper, we study generalized symmetric Finsler spaces. We first study symmetry preserving diffeomorphisms, then we show that the group of symmetry preserving diffeomorphisms is a transitive Lie transformation group. Finally we give some existence theorems.